Computer modeling of catalytic effects of a series of the transition metals and their alloys on the process of dissociation of molecular hydrogen has been performed. The project was composed of three stages. First, the binding energy versus the internuclear distance has been calculated for a series of metal dimers and mixed dimers: Ni-2, NiCu, Cu-2, Ag-2, AgPd, Pd-2. Then, using the fitted Morse form of the potential interaction between the metal atoms, the Molecular Dynamics (MD) simulations have been performed in order to obtain the atomic structures appearing in the alloys. The third part of the project includes the quantum-chemical calculations of hydrogen atom and hydrogen molecule positioned over the metallic dimers. The interatomic distances of the dimers were taken from the MD calculations. A range of the distances of hydrogen from the metal dimers was scanned. The evolution of energy and electron density with the hydrogen distance from certain dimers, like NiCu, AgPd and Pd-2, clearly exhibits the process of the hydrogen molecule dissociation. On a basis of these calculations a measure of catalytic power of the metals was defined and the series of metals and alloys was ordered according to their catalytic power. It was found that the highest catalytic power with respect to the hydrogen dissociation process is exhibited by NiCu alloys. All the quantum-chemical calculations have been performed using the methods of the density functional theory (DFT). The nonlocal version of the DFT was applied with the gradient-corrected functionals for electron exchange and correlation. The GAUSSIAN-94 and -98 suites of programs were employed in the calculations.